What is the Alpha Convert node used for?
It's used for manually converting between Straight and Premultiplied alpha.
This is sometimes needed when using external images in compositing, among other uses.
See the wiki:

Straight Alpha
This is the alpha type used by paint programs such as Photoshop or
Gimp, and used in common file formats like PNG, BMP or Targa. So,
image textures or output for the web are usually straight alpha. RGBA
color are stored as (R, G, B, A) channels, with the RGB channels
unaffected by the alpha channels.
Premultiplied Alpha
Rendering will output premultiplied alpha images, and the OpenEXR file
format uses this alpha type. So, intermediate files for rendering and
compositing are often stored as premultiplied alpha. Compared to
straight alpha, the colors could be considered to be stored as (R*A,
G*A, B*A, A), with the alpha multiplied into the RGB channel.
This is the natural output of render engines, with the RGB channels
representing the amount of light that comes toward the viewer, and
alpha representing how much of the light from the background is
blocked.
Conversion
Conversion between the two alpha types is not a simple operation and
can involve data loss, as both alpha types can represent data that the
other can not, though it is often subtle.
Straight alpha can be considered to be an RGB color image with a
separate alpha mask. In areas where this mask is fully transparent,
there can still be colors in the RGB channels. On conversion to
premultiplied alpha this mask is 'applied' and the colors in such
areas become black and are lost.
Premultiplied alpha on the other hand can represent renders that are
both emitting light and letting through light from the background. For
example a transparent fire render might be emitting light, but also
letting through all light from objects behind it. On converting to
straight alpha this effect is lost.